The trouble with teaching one's self anything is that the established methods of doing it are probably beyond what any individual could figure out by himself in his lifetime. Despite their genius, Mozart, Beethoven, and even the profound Liszt and Chopin were at one time aided by the teachers who gave them the necessary musical foundation upon which they later built. Without this fundamental help, perhaps they would have excelled in a race of self-apprenticeship among average people. But even with their innate brilliance, because of the infinitely broad scope of piano mastery, it's likely that they would have developed quite poorly next to an average person intimately trained under a competent teacher possessing the sum of human knowledge on the subject.
If you were to venture into piano study on your own, it's very likely that you'll be lacking the wherewithal to do it properly in many aspects. You will most likely endure years of trial-and-error that would, and should, be skipped altogether with a teacher's guidance. Also, much of piano technique, and even music theory, is counter-intuitive, which means you will be doing the opposite of what you should be doing much of the time, resulting in poor, possibly damaging technique and counter-productive training overall. Even though it being difficult or even impossible to get a good piano teacher is certainly understandable, the reality is you will already be with somewhat a huge handicap. Having said that, self-teaching pianists need to be extra careful and mindful of the practice methods they develop for themselves.
First in order is a good book for beginner pianists. I don't recommend risking time and money on any of the multitude of online or TV piano learning products -- even though some of them might be good -- because the Alfred's paperback series has already been around forever and is fairly ubiquitous in the formal piano learning environment. Get your hands on the Level One book for adults and move your way through the series from there. You can find a number of different Alfred's titles for adult beginners at Amazon.com. Any music store should also have the collection readily available. If you would like to shop for alternatives, do so, but cautiously. It is important that they are well received. A good piano book will typically be widely evaluated and should have many positive customer reviews, particularly from piano teachers.
When studying with books, you have to make an effort to take your time. Because you have the entire book at your disposal, you might be inclined to rush through, or completely over, certain chapters as you so choose. As a teacher, submitting your lessons to your student's discretion would be dangerous. As a student, especially if you are a beginning student, be mindful of your general lack of knowledge in the subject and regard every detail of your learning materials with respect and importance. In good piano books, the lessons are thoughtfully arranged and every exercise is meant to teach you something or enhance your mechanical technique. In teacher-student lessons, it's not that uncommon that entire weeks are spent on single pages of piano learning books because the student hasn't quite grasped and perfected the exercise. Keep this in mind as you study, and make an effort to pace yourself, especially when you are challenged.
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